Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53REIn Problems , use and .
Find the distance from to .
In Problems , use and .
Find the midpoint of line segment joining and .
In Problems , use and .
(a) Find the slope of the line containing and .
(b) Interpret this slope.
In Problems , use and .
Graph by plotting points.
In Problems , use and .
Graph .
In Problems , use and .
List the intercepts and test for symmetry: .
In Problems , use and .
Write the slope-intercept form of the line with slope -2 containing the point . Graph the line.
8CT9CTIn Problems 13, use P1=(1,3) and P2=(5,1). For the line 2x+3y=6, find a line parallel to the given line containing the point (1,1). Also find a line perpendicular to the given line containing the point (0,3).1. On a real number line the origin is assigned the number _____ .2. If 3 and 5 are the coordinates of two points on the real number line, the distance between these points is _____ .3. If 3 and 4 are the legs of a right triangle, the hypotenuse is _____ .4. Use the converse of the Pythagorean Theorem to show that a triangle whose sides are of lengths 11, 60 and 61 is a right triangle.5. The area of a triangle whose base is b and whose altitude is h is A= _____ .6. True or False Two triangles are congruent if two angles and the included side of one equals two angles and the included side of the other.7. If ( x,y ) are the coordinates of a point P in the xy-plane , then x is called the _____ of P and y is the _____ of P .8. The coordinate axes divide the xy-plane into four sections called _____ .9. If three distinct points P , Q and R all lie on a line and if d( P,Q )=d(Q,R) , then Q is called the _____ of the line segment from P to R .10. True or False The distance between two points is sometimes a negative number.11. True or False The point (1,4) lies in quadrant IV of the Cartesian plane.12. True or False The midpoint of a line segment is found by averaging the x-coordinates and averaging the y-coordinates of the endpoints.In Problems 15 and 16, plot each point in the xy-plane . Tell in which quadrant or on what coordinate axis each point lies. 15. (a) A=( 3,2 ) (b) B=( 6,0 ) (c) C=( 2,2 ) (d) D=( 6,5 ) (e) E=( 0,3 ) (f) F=( 6,3 )In Problems 15 and 16, plot each point in the xy-plane . Tell in which quadrant or on what coordinate axis each point lies. 16. (a) A=( 1,4 ) (b) B=( 3,4 ) (c) C=( 3,4 ) (d) D=( 4,1 ) (e) E=( 0,1 ) (f) F=( 3,0 )17. Plot the points ( 2,0 ),( 2,3 ),( 2,4 ),(2,1) and ( 2,1 ) . Describe the set of all points of the form ( 2,y ) , where y is a real number.18. Plot the points ( 0,3 ),( 1,3 ),( 2,3 ),(5,3) and ( 4,3 ) . Describe the set of all points of the form ( x,3 ) , where x is a real number.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 35.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 36.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 37.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 38.21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYUIn Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 51. A=( 2,5 );B=( 1,3 );C=( 1,0 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 52. A=( 2,5 );B=( 12,3 );C=( 10,11 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 53. A=( 5,3 );B=( 6,0 );C=( 5,5 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 54. A=( 6,3 );B=( 3,5 );C=( 1,5 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 55. A=( 4,3 );B=( 0,3 );C=( 4,2 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 56. A=( 4,3 );B=( 4,1 );C=( 2,1 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . 57. P 1 =( 3,4 ); P 2 =( 5,4 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . 58. P 1 =( 2,0 ); P 2 =( 2,4 )In Problemsfind the midpoint of the line segment joining the pointsand.
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In Problems 3946 find the midpoint of the line segment joining the points P1 and P2. P1=(2,3);P2=(4,2)In Problems 3946 find the midpoint of the line segment joining the points P1 and P2. P1=(7,5);P2=(9,1)In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . P 1 =( 4,3 ); P 2 =( 2,2 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . P 1 =( a,b ); P 2 =( 0,0 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . P 1 =( a,a ); P 2 =(0,0)If the point (2,5) is shifted 3 units to the right and 2 units down, what are its new coordinates?If the point (1,6) is shifted 2 units to the left and 4 units up, what are its new coordinates?Find all points having an-coordinate ofwhose distance from the pointis.
By using the Pythagorean Theorem.
By using the distance formula.
Find all points having a-coordinate ofwhose distance from the pointis
By using the Pythagorean Theorem.
By using the distance formula.
Find all points on the x-axis that are 6 units from the point (4,3).Find all points on the-axis that areunits from the point.
Suppose thatare the coordinates of a point in the-plane.
Find the coordinates of the point ifis shiftedunits to the left andunits down.
Find the coordinates of the point ifis shiftedunits to the left andunits up.
Plot the pointsandin the-plane. Ifis the midpoint of a line segment, find the coordinates of.
The midpoint of the line segment from P1 to P2 is (1,4). If P1=(3,6), what is P2?The midpoint of the line segment fromtois. If, what is?
The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side (see the figure). Find the lengths of the medians of the triangle with vertices at A=( 0,0 ),B=( 6,0 ),andC=( 4,4 ) .An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are ( 0,4 )and( 0,0 ) , find the third vertex. How many of these triangles are possible?In Problems 103-106, find the length of each side of the triangle determined by the three points P 1 , P 2 ,and P 3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P 1 =( 2,1 ); P 2 =( 4,1 ); P 3 =( 4,3 )In Problems 103-106, find the length of each side of the triangle determined by the three points P 1 , P 2 ,and P 3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P 1 =(1,4); P 2 =(6,2); P 3 =(4,5)In Problems 103-106, find the length of each side of the triangle determined by the three points P 1 , P 2 ,and P 3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P 1 =( 2,1 ); P 2 =( 0,7 ); P 3 =( 3,2 )In Problems 103-106, find the length of each side of the triangle determined by the three points P 1 , P 2 ,and P 3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P 1 =( 7,2 ); P 2 =( 4,0 ); P 3 =( 4,6 )Baseball A major league baseball “diamond� is actually a square, 90 feet on a side (see the figure). What is the distance directly from home plate to second base (the diagonal of the square)?Little league Baseball The layout of a Little League playing field is a square, 60 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? Source: Little League Baseball, Official Regulations and Playing Rules, 2014.Baseball Refer to Problem 63. Overlay a rectangular coordinate system on a major league baseball diamond so that the origin is at home plate, the positive x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base. What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement. If the right fielder is located at (310,15) how far is it from the right fielder to second base? If the center fielder is located at (300,300), how far is it from the center fielder to third base?Little league Baseball Refer to Problem 64. Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base. What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement. If the right fielder is located at (180,20) how far is it from the right fielder to second base? If the center fielder is located at (220,220), how far is it from the center fielder to third base?Distance between Moving Objects A Ford Focus and a Freightliner Cascadia truck leave an intersection at the same time. The Focus heads east at an average speed ofmiles per hour, while the Cascadia heads south at an average speed ofmiles per hour. Find an expression for their distance apart (in miles) at the end ofhours.
Distance of a Moving Object from a Fixed Point A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 100 feet, passes over an intersection (see the figure). Find an expression for its distance d (measured in feet) from the intersection t seconds later.Drafting Error When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequently will form an error triangle. If this error triangle is long and thin, one estimate for the location of the desired point is the midpoint of the shortest side. The figure shows one such error triangle. Find an estimate for the desired intersection point. Find the distance from (1.4,1.3) to the midpoint found in part (a).Net Sales The figure illustrates the net sales growth of Costco Wholesale Corporation from 2013 through 2017. Use the midpoint formula to estimate the net sales of Costco Wholesale Corporation in 2015. How does your result compare to the reported value of 113.67 billion?Poverty Threshold Poverty thresholds are determined by the U.S. Census Bureau. A poverty threshold represents the minimum annual household income for a family not to be considered poor. In, the poverty threshold for a family of four with two children under the age ofyears was. In, the poverty threshold for a family of four with two children under the age ofyears was.Assuming that poverty thresholds increase in a straight-line fashion use the midpoint formula to estimate the poverty threshold for a family of four with two children under the age ofin. How does your result compare to the actual poverty threshold inof?
Write a paragraph that describes a Cartesian plane. Then write a second paragraph that describes how to plot points in the Cartesian plane. Your paragraphs should include the terms “coordinate axes,� “ordered pair,� “coordinates,� “plot,� “ x-coordinate ,� and “ y-coordinate .�Solve: 2( x+3 )1=7 (pp. A44-A46)Solve the equation x29=0The points, if any, at which a graph crosses or touches the coordinate axes are called _______.The -intercepts of the graph of an equation are those -values for which________.
5AYU6AYU7AYUTrue or False To find the y-intercepts of the graph of an equation, let x=0 and solve for y .True or False The-coordinate of a point at which the graph crosses or touches the -axis is an -intercept.
True or False If a graph is symmetric with respect to the x-axis , then it cannot be symmetric with respect to the y-axis .In Problems, determine which of the given points are on the graph of the equation.
Equation:
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In Problems 1318, determine which of the given points are on the graph of the equation. Equation: y=x32x Points: (0,0);(1,1);(1,1).In Problems, determine which of the given points are on the graph of the equation.
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In Problems 1318, determine which of the given points are on the graph of the equation. Equation: y3=x+1 Points: (1,2);(0,1);(1,0).In Problems 1318, determine which of the given points are on the graph of the equation. Equation: x2+y2=4 Points: (0,2);(2,2);(2,2).In Problems 1318, determine which of the given points are on the graph of the equation. Equation: x2+4y2=4 Points: (0,1);(2,0);(2,12).In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y=x+2In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y=x6In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y=2x+8In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y=3x9In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y= x 2 1In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y= x 2 9In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y= x 2 +4In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y= x 2 +1In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 2x+3y=6In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 5x+2y=10In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 9 x 2 +4y=36In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 4 x 2 +y=4In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (3,4)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (5,3)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (2,1)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (4,2)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (5,2)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (1,1)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (3,4)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (4,0)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (0,3)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (3,0)In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.51AYU52AYU53AYU54AYUIn Problems 5772, list the intercepts and test for symmetry. y2=x+16In Problems 49-64, list the intercepts and test for symmetry. y 2 =x+9In Problems 49-64, list the intercepts and test for symmetry. y= x 3In Problems 49-64, list the intercepts and test for symmetry. y= x 5In Problems 5772, list the intercepts and test for symmetry. x2+y9=0In Problems 5772, list the intercepts and test for symmetry. x2y4=0In Problems, list the intercepts and test for symmetry.
In Problems 49-64, list the intercepts and test for symmetry. 4 x 2 + y 2 =4In Problems, list the intercepts and test for symmetry.
In Problems 49-64, list the intercepts and test for symmetry. y= x 4 1In Problems, list the intercepts and test for symmetry.
In Problems 49-64, list the intercepts and test for symmetry. y= x 2 +4In Problems 5772, list the intercepts and test for symmetry. y=4xx2+16In Problems 49-64, list the intercepts and test for symmetry. y= x 2 4 2xIn Problems 49-64, list the intercepts and test for symmetry. y= x 3 x 2 9In Problems 49-64, list the intercepts and test for symmetry. y= x 4 4 +1 2 x 5In Problems 65-68, draw a quick sketch of each equation. y= x 3In Problems 65-68, draw a quick sketch of each equation. x= y 2In Problems 65-68, draw a quick sketch of each equation. y= xIn Problems 65-68, draw a quick sketch of each equation. y= 1 x75AYU76AYU77AYU78AYU79AYUIf the graph of an equation is symmetric with respect to the y-axis and 6 is an x-intercept of this graph, name another x-intercept .If the graph of an equation is symmetric with respect to the origin and 4 is an x-intercept of this graph, name another x-intercept .If the graph of an equation is symmetric with respect to the x-axis and 2 is a y-intercept , name another x-intercept .Microphones n studios and on stages, cardioid microphones are often preferred for the richness they add to voices and for their ability to reduce the level of sound from the sides and rear of the microphone. Suppose one such cardioid pattern is given by the equation ( x 2 + y 2 x ) 2 = x 2 + y 2 . a. Find the intercepts of the graph of the equation. b. Test for symmetry with respect to the x-axis , y-axis , and origin. Source: www.notaviva.comSolar Energy The solar electric generating systems at Kramer Junction, California, use parabolic troughs to heat a heat-transfer fluid to a high temperature. This fluid is used to generate steam that drives a power conversion system to produce electricity. For troughs 7.5 feet wide, an equation for the cross-section is 16 y 2 =120x225 . a. Find the intercepts of the graph of the equation. b. Test for symmetry with respect to the x-axis , y-axis , and origin. Source: U.S. Department of Energy
Graph,,and,noting which graphs are the same.
Explain why the graphs ofandare the same.
Explain why the graphs ofandare not the same.
Explain why the graphs ofandare not the same.
Explain what is meant by a complete graph.Draw a graph of an equation that contains two x-intercepts at one the graph crosses the x-axis , and at the other the graph touches the x-axis .Make up an equation with the intercepts,and. Compare your equation with a friend’s equation. Comment on any similarities.
Draw a graph that contains the points ( 2,1 ) , ( 0,1 ) , ( 1,3 ) , and ( 3,5 ) . Compare your graph with those of other students. Are most of the graphs almost straight lines? How many are “curved�? Discuss the various ways that these points might be connected.90AYUDraw a graph that contains the points ( 2,5 ) , ( 1,3 ) , and ( 0,2 ) that is symmetric with respect to the y-axis . Compare your graph with those of other students; comment on any similarities. Can a graph contain these points and be symmetric with respect to the x-axis ? the origin? Why or why not?92AYU93AYU94AYU1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYUIn Problems 13-16, (a) find the slope of the line and (b) interpret the slope.In Problems 13-16, (a) find the slope of the line and (b) interpret the slope.In Problems 13-16, (a) find the slope of the line and (b) interpret the slope.In Problems 13-16, (a) find the slope of the line and (b) interpret the slope.In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (2,3);(4,0)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (4,2);(3,4)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (2,3);(2,1)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (1,1);(2,3)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (3,1);(2,1)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (4,2);(5,2)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (1,2);(1,2)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (2,0);(2,2)In Problems 25-32, graph the line containing the point P and having slope m . P=( 1,2 );m=3In Problems 25-32, graph the line containing the point P and having slope m . P=( 2,1 );m=4In Problems 25-32, graph the line containing the point P and having slope m . P=( 2,4 );m= 3 4In Problems 25-32, graph the line containing the point P and having slope m . P=( 1,3 );m= 2 5In Problems 25-32, graph the line containing the point P and having slope m . P=( 1,3 );m=0In Problems 25-32, graph the line containing the point P and having slope m . P=( 2,4 );m=029AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYUIn Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope =3 ; containing the point ( 2,3 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope =2 ; containing the point ( 4,3 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope = 1 2 ; containing the point ( 3,1 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope = 2 3 ; containing the point ( 1,1 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Containing the points ( 1,3 )and( 1,2 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Containing the points ( 3,4 )and( 2,5 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope =3 ; y-intercept=3In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope=-2;y-intercept=-2In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. x-intercept=4;y-intercept=4In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. x-intercept=2;y-intercept=1In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope undefined; containing the point ( 2,4 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope undefined; containing the point ( 3,8 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Horizontal; containing the point ( 3,2 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Vertical; containing the point ( 4,5 )In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line y=2x; containing the point (1,2)In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line y=3x ; containing the point (1,2)In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line x2y=5 ; containing the point ( 0,0 )In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line 2xy=2; containing the point (0,0)In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line x=5 ; containing the point ( 4,2 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line y=5 ; containing the point ( 4,2 )In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line y=12x+4; containing the point (1,2)In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line y=2x3; containing the point (1,2)In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line x2y=5; containing the point (0,4)In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line 2x+y=2; containing the point (3,0)In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line x=8 ; containing the point ( 3,4 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line y=8 ; containing the point ( 3,4 )In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y=2x+3In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y=3x+4In Problems 7998, find the slope and y-intercept of each line. Graph the line. 12y=x1In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. 1 3 x+y=2In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y= 1 2 x+2